/** * @FileName a.cpp * @Author kanpurin * @Created 2020.10.31 00:03:56 **/ #include "bits/stdc++.h" using namespace std; typedef long long ll; template< int MOD > struct mint { public: long long x; mint(long long x = 0) :x((x%MOD+MOD)%MOD) {} mint(std::string &s) { long long z = 0; for (int i = 0; i < s.size(); i++) { z *= 10; z += s[i] - '0'; z %= MOD; } this->x = z; } mint& operator+=(const mint &a) { if ((x += a.x) >= MOD) x -= MOD; return *this; } mint& operator-=(const mint &a) { if ((x += MOD - a.x) >= MOD) x -= MOD; return *this; } mint& operator*=(const mint &a) { (x *= a.x) %= MOD; return *this; } mint& operator/=(const mint &a) { long long n = MOD - 2; mint u = 1, b = a; while (n > 0) { if (n & 1) { u *= b; } b *= b; n >>= 1; } return *this *= u; } mint operator+(const mint &a) const { mint res(*this); return res += a; } mint operator-() const {return mint() -= *this; } mint operator-(const mint &a) const { mint res(*this); return res -= a; } mint operator*(const mint &a) const { mint res(*this); return res *= a; } mint operator/(const mint &a) const { mint res(*this); return res /= a; } friend std::ostream& operator<<(std::ostream &os, const mint &n) { return os << n.x; } friend std::istream &operator>>(std::istream &is, mint &n) { long long x; is >> x; n = mint(x); return is; } bool operator==(const mint &a) const { return this->x == a.x; } bool operator!=(const mint &a) const { return this->x != a.x; } mint pow(long long k) const { mint ret = 1; mint p = this->x; while (k > 0) { if (k & 1) { ret *= p; } p *= p; k >>= 1; } return ret; } }; constexpr int MOD = 1e9 + 7; template< class T > struct Matrix { std::vector< std::vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, std::vector< T >(m, 0)) {} Matrix(size_t n) : A(n, std::vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const std::vector< T > &operator[](int k) const { return (A.at(k)); } inline std::vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); std::vector< std::vector< T > > C(n, std::vector< T >(m, 0)); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) for (int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } bool operator==(const Matrix &B) const { assert(this->A.size() == B.A.size() && this->A[0].size() == B.A[0].size()); int n = this->A.size(); int m = this->A[0].size(); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (this->A[i][j] != B.A[i][j]) return false; return true; } bool operator!=(const Matrix &B) const { return !(*this == B); } friend std::ostream &operator<<(std::ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for (int i = 0; i < n; i++) { os << "["; for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for (int i = 0; i < width(); i++) { int idx = -1; for (int j = i; j < width(); j++) { if (B[j][i] != 0) idx = j; } if (idx == -1) return (0); if (i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for (int j = 0; j < width(); j++) { B[i][j] /= vv; } for (int j = i + 1; j < width(); j++) { T a = B[j][i]; for (int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } Matrix pow(ll k) const { auto res = I(A.size()); auto M = *this; while (k > 0) { if (k & 1) { res *= M; } M *= M; k >>= 1; } return res; } }; int main() { ll a,b,n;cin >> a >> b >> n; if (n == 0) { cout << 2 << endl; return 0; } else if (n == 1) { cout << 2 * a % MOD << endl; return 0; } Matrix> mat(2); mat[0][0] = mint(2 * a), mat[0][1] = mint(-a*a+b); mat[1][0] = 1; mat = mat.pow(n-1); cout << mat[0][0] * 2 * a + mat[0][1] * 2 << endl; return 0; }